Quantum theory of a double-well potential: Energy levels for symmetric and nonsymmetric double-well potentials in a three-dimensional system

Energy eigenvalues are obtained for a double-well potential V(x, y, z; Zx2, Zy2, Zz2, λ) = −12[Zx2x2 + Zy2y2 + Zz2z2] + λ[axxx4 + ayyy4 + azzz4 + 2axyx2y2 + 2axzx2z2 + 2ayzy2z2], in a three-dimensional system, using matrix diagonalization, for various values of parameters Zx2, Zy2, Zz2, λ and several energy levels Enx,ny,nz. Comparison is made with results obtained by other means.